Low-frequency breakdown of the potential integral equations and its remedy

Potential integral equations (PIEs) introduced recently also have a low-frequency breakdown that becomes visible when considering the electric charge density and near-zone electric field intensity values. As opposed to the well-known low-frequency breakdown of the electric-field integral equation (EFIE), which shows itself as both inaccuracy and ill-conditioning, the low-frequency breakdown of PIEs is not related to the conditioning properties of the related matrix equations. Therefore, we clearly distinguish the low-frequency breakdowns of EFIE and PIEs by categorizing the underlying mechanisms as field imbalance and source imbalance. Numerical examples are presented to provide a complete picture of these integral equations at low-frequencies, besides an effective post-processing method to mitigate the inaccuracies in PIEs.